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Journal articles on the topic 'Multi-Scale nonlinear dynamics'

Author: Grafiati

Published: 14 December 2024

Last updated: 31 July 2025

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1

Sivapalan, Murugesu, Praveen Kumar, and Daniel Harris. "Nonlinear propagation of multi-scale dynamics through hydrologic subsystems." Advances in Water Resources 24, no. 9-10 (2001): 935–40. http://dx.doi.org/10.1016/s0309-1708(01)00028-8.

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LAMARQUE, C. H., A. TURE SAVADKOOHI, E. ETCHEVERRIA, and Z. DIMITRIJEVIC. "MULTI-SCALE DYNAMICS OF TWO COUPLED NONSMOOTH SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 12 (2012): 1250295. http://dx.doi.org/10.1142/s0218127412502951.

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Dynamical behavior of a nonsmooth master system which is coupled to a nonsmooth Nonlinear Energy Sink (NES) during free and forced oscillations is studied analytically and numerically. Invariant manifolds of the system and their stable zones at different time scales are revealed and finally application of coupled nonsmooth NES to the passive control process of the main nonsmooth system is highlighted.

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Bartelt, Matthias, and Michael Groß. "Galerkin-based multi-scale time integration for nonlinear structural dynamics." PAMM 14, no. 1 (2014): 215–16. http://dx.doi.org/10.1002/pamm.201410095.

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4

Wu, Zhe, Guang Yang, Qiang Zhang, Shengyue Tan, and Shuyong Hou. "Information Dynamic Correlation of Vibration in Nonlinear Systems." Entropy 22, no. 1 (2019): 56. http://dx.doi.org/10.3390/e22010056.

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In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we pr

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Jiang, H., X. Gao, Y. Sheng, W. Tang, and P. Shi. "Analysis of 3:1 internal resonance of a rigid-flexible coupling antenna system with three degrees of freedom." Journal of Physics: Conference Series 3041, no. 1 (2025): 012006. https://doi.org/10.1088/1742-6596/3041/1/012006.

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Abstract This paper investigates the nonlinear dynamic behavior of a spatially deployable antenna’s rigid-flexible coupling structure. Firstly, a three-degree-of-freedom T-beam structure model consisting of a rigid manipulator and a symmetrical antenna is established. By applying the Lagrange equation and the assumed modes method, the governing nonlinear dynamics equations for the T-beam’s in-plane motion are formulated. Subsequently, the system’s nonlinear dynamic behavior under 3:1 internal resonance conditions is investigated employing the matrix-form multi-scale methodology. The general ex

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KOVALEV, VLADIMIR F. "LIE GROUP ANALYSIS FOR MULTI-SCALE PLASMA DYNAMICS." Journal of Nonlinear Mathematical Physics 18, sup1 (2011): 163–75. http://dx.doi.org/10.1142/s1402925111001349.

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7

KUSKE, R. "MULTI-SCALE DYNAMICS IN STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH MULTIPLICATIVE NOISE." Stochastics and Dynamics 05, no. 02 (2005): 233–46. http://dx.doi.org/10.1142/s0219493705001390.

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We apply multi-scale analysis to stochastic delay-differential equations with multiplicative or parametric noise, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays. Reduced equations for the envelope of the oscillations provides an efficient analysis of the dynamics by separating the influence of the noise from the intrinsic oscillations over long time scales. We show how this analysis can be used to compute Lyapunov exponents and extended to nonlinear models where the noise has additional resonances.

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Knar, Zakaria, Jean-Jacques Sinou, Sébastien Besset, and Vivien Clauzon. "An Adapted Two-Steps Approach to Simulate Nonlinear Vibrations of Solid Undergoing Large Deformation in Contact with Rigid Plane—Application to a Grooved Cylinder." Applied Sciences 12, no. 3 (2022): 1447. http://dx.doi.org/10.3390/app12031447.

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Simulating the full dynamic response of a rolling sculpted tire requires not only taking into account various non-linearities but also considering the multi-scale nature of the dynamic response itself. On one hand, there is the macroscopic rolling dynamic behavior that operates around the rotating frequency with relatively high amplitudes. On the other hand, the vibratory response operates in a larger frequency window with relatively low amplitudes. In contrast to a straightforward strategy that consists of using an energy-conserving stable time integrator to predict the multi-scale dynamic re

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Overwiening, Jorin, Federico Tesler, Domenico Guarino, and Alain Destexhe. "A multi-scale study of thalamic state-dependent responsiveness." PLOS Computational Biology 20, no. 12 (2024): e1012262. https://doi.org/10.1371/journal.pcbi.1012262.

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The thalamus is the brain’s central relay station, orchestrating sensory processing and cognitive functions. However, how thalamic function depends on internal and external states, is not well understood. A comprehensive understanding would necessitate the integration of single cell dynamics with their collective behavior at population level. For this we propose a biologically realistic mean-field model of the thalamus, describing thalamocortical relay neurons (TC) and thalamic reticular neurons (RE). We perform a multi-scale study of thalamic responsiveness and its dependence on cell and brai

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Rundle, J. B., D. L. Turcotte, P. B. Rundle, et al. "Pattern dynamics, pattern hierarchies, and forecasting in complex multi-scale earth systems." Hydrology and Earth System Sciences Discussions 3, no. 3 (2006): 1045–69. http://dx.doi.org/10.5194/hessd-3-1045-2006.

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Abstract. Catastrophic disasters afflicting human society are often triggered by tsunamis, earthquakes, widespread flooding, and weather and climate events. As human populations increasingly move into geographic areas affected by these earth system hazards, forecasting the onset of these large and damaging events has become increasingly urgent. In this paper we consider the fundamental problem of forecasting in complex multi-scale earth systems when the basic dynamical variables are either unobservable or incompletely observed. In such cases, the forecaster must rely on incompletely determined

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Rundle, J. B., D. L. Turcotte, P. B. Rundle, et al. "Pattern dynamics, pattern hierarchies, and forecasting in complex multi-scale earth systems." Hydrology and Earth System Sciences 10, no. 6 (2006): 789–96. http://dx.doi.org/10.5194/hess-10-789-2006.

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Abstract. Catastrophic disasters afflicting human society are often triggered by tsunamis, earthquakes, widespread flooding, and weather and climate events. As human populations increasingly move into geographic areas affected by these earth system hazards, forecasting the onset of these large and damaging events has become increasingly urgent. In this paper we consider the fundamental problem of forecasting in complex multi-scale earth systems when the basic dynamical variables are either unobservable or incompletely observed. In such cases, the forecaster must rely on incompletely determined

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Quaranta, Giuseppe, Giovanni Formica, J. Tenreiro Machado, Walter Lacarbonara, and Sami F. Masri. "Understanding COVID-19 nonlinear multi-scale dynamic spreading in Italy." Nonlinear Dynamics 101, no. 3 (2020): 1583–619. http://dx.doi.org/10.1007/s11071-020-05902-1.

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Abstract The outbreak of COVID-19 in Italy took place in Lombardia, a densely populated and highly industrialized northern region, and spread across the northern and central part of Italy according to quite different temporal and spatial patterns. In this work, a multi-scale territorial analysis of the pandemic is carried out using various models and data-driven approaches. Specifically, a logistic regression is employed to capture the evolution of the total positive cases in each region and throughout Italy, and an enhanced version of a SIR-type model is tuned to fit the different territorial

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MAJDA, ANDREW J., YULONG XING, and MAJID MOHAMMADIAN. "Moist multi-scale models for the hurricane embryo." Journal of Fluid Mechanics 657 (June 30, 2010): 478–501. http://dx.doi.org/10.1017/s0022112010001515.

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Determining the finite-amplitude preconditioned states in the hurricane embryo, which lead to tropical cyclogenesis, is a central issue in contemporary meteorology. In the embryo there is competition between different preconditioning mechanisms involving hydrodynamics and moist thermodynamics, which can lead to cyclogenesis. Here systematic asymptotic methods from applied mathematics are utilized to develop new simplified moist multi-scale models starting from the moist anelastic equations. Three interesting multi-scale models emerge in the analysis. The balanced mesoscale vortex (BMV) dynamic

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14

Hajjaj, Amal Z., Jonathan Ortiz, and Abdessattar Abdelkefi. "Nonlinear size-dependent modeling and dynamics of nanocrystalline arc resonators." International Journal of Mechanics and Materials in Design 18, no. 1 (2021): 105–23. http://dx.doi.org/10.1007/s10999-021-09574-6.

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AbstractThe adequate modeling of the micro/nano arc resonators' dynamics is vital for their successful implementation. Here, a size-dependent model, wherein material structure, porosity, and micro-rotation effects of the grains are considered, is derived by combining the couple stress theory, multi-phase model, and the classical Euler–Bernoulli beam model, aiming to characterize the frequency tunability of micro/nano arc resonators as monitoring either the axial load or the electrostatic force for the first time. The arc dimensions are optimized to show various phenomena in the same arc, namel

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15

Su, C. H., and D. Ryu. "Multi-scale analysis of bias correction of soil moisture." Hydrology and Earth System Sciences Discussions 11, no. 7 (2014): 8995–9026. http://dx.doi.org/10.5194/hessd-11-8995-2014.

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Abstract. Remote sensing, in situ networks and models are now providing unprecedented information for environmental monitoring. To conjunctively use multi-source data nominally representing an identical variable, one must resolve biases existing between these disparate sources, and the characteristics of the biases can be non-trivial due to spatiotemporal variability of the target variable, inter-sensor differences with variable measurement supports. One such example is of soil moisture (SM) monitoring. Triple collocation (TC) based bias correction is a powerful statistical method that increas

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16

Lyu, Weipeng, Shaolong Li, Zhenyang Chen, and Qinsheng Bi. "Bursting Dynamics in a Singular Vector Field with Codimension Three Triple Zero Bifurcation." Mathematics 11, no. 11 (2023): 2486. http://dx.doi.org/10.3390/math11112486.

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As a kind of dynamical system with a particular nonlinear structure, a multi-time scale nonlinear system is one of the essential directions of the current development of nonlinear dynamics theory. Multi-time scale nonlinear systems in practical applications are often complex forms of coupling of high-dimensional and high codimension characteristics, leading to various complex bursting oscillation behaviors and bifurcation characteristics in the system. For exploring the complex bursting dynamics caused by high codimension bifurcation, this paper considers the normal form of the vector field wi

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17

Armand, J., L. Pesaresi, L. Salles, C. Wong, and C. W. Schwingshackl. "A modelling approach for the nonlinear dynamics of assembled structures undergoing fretting wear." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2223 (2019): 20180731. http://dx.doi.org/10.1098/rspa.2018.0731.

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Assembled structures tend to exhibit nonlinear dynamic behaviour at high excitation levels due to the presence of contact interfaces. The possibility of building predictive models relies on the ability of the modelling strategy to capture the complex nonlinear phenomena occurring at the interface. One of these phenomena, normally neglected, is the fretting wear occurring at the frictional interface. In this paper, a computationally efficient modelling approach which enables considerations of the effect of fretting wear on the nonlinear dynamics is presented. A multi-scale strategy is proposed,

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18

Wei, Liran, Mingzhu Tang, Na Li, Jingwen Deng, Xinpeng Zhou, and Haijun Hu. "Multifractal-Aware Convolutional Attention Synergistic Network for Carbon Market Price Forecasting." Fractal and Fractional 9, no. 7 (2025): 449. https://doi.org/10.3390/fractalfract9070449.

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Accurate carbon market price prediction is crucial for promoting a low-carbon economy and sustainable engineering. Traditional models often face challenges in effectively capturing the multifractality inherent in carbon market prices. Inspired by the self-similarity and scale invariance inherent in fractal structures, this study proposes a novel multifractal-aware model, MF-Transformer-DEC, for carbon market price prediction. The multi-scale convolution (MSC) module employs multi-layer dilated convolutions constrained by shared convolution kernel weights to construct a scale-invariant convolut

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19

Li, Hong-Wei, Ting Wang, Chang Chang, Bin Sun, Wen-peng Hong, and Yun-long Zhou. "Multi-scale nonlinear analysis of drying dynamics in the mixed pulsed drying fluidized beds." Powder Technology 339 (November 2018): 958–69. http://dx.doi.org/10.1016/j.powtec.2018.08.078.

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Montegiglio, Pasquale, Claudio Maruccio, Giuseppe Acciani, Gianluca Rizzello, and Stefan Seelecke. "Nonlinear multi-scale dynamics modeling of piezoceramic energy harvesters with ferroelectric and ferroelastic hysteresis." Nonlinear Dynamics 100, no. 3 (2020): 1985–2003. http://dx.doi.org/10.1007/s11071-020-05660-0.

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21

Liu, Zhifeng, Kai Liu, Chuanhai Chen, Siwei Lu, Hanyu Wang, and Li Yin. "Similitude-based construction of scaled crane boom models via finite element analysis." Journal of Physics: Conference Series 3033, no. 1 (2025): 012034. https://doi.org/10.1088/1742-6596/3033/1/012034.

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Abstract This study presents a novel cross-scale equivalent modeling methodology for the boom structure of truck-mounted cranes. Based on the principles of dimensional analysis and differential equation theory, the proposed approach establishes a framework for geometry-dynamics similarity criteria. By integrating dynamic response equivalence criteria with displacement similarity principles, the method refines the model through multi-case simulations and nonlinear regression techniques. This process effectively mitigates mechanical response distortions caused by scale effects and structural non

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22

Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysi

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23

Hou, Shuangshan, Jinde Zheng, Haiyang Pan, Ke Feng, Qingyun Liu, and Qing Ni. "Multivariate multi-scale cross-fuzzy entropy and SSA-SVM-based fault diagnosis method of gearbox." Measurement Science and Technology 35, no. 5 (2024): 056102. http://dx.doi.org/10.1088/1361-6501/ad2053.

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Abstract Fuzzy entropy (FuzzyEn) is widely recognized as a powerful tool for analyzing nonlinear dynamics and measuring the complexity of time series data. It has been utilized as an effective indicator to capture nonlinear fault features in gearbox vibration signals. However, FuzzyEn only measures complexity at a single scale, ignoring the valuable information contained in large-scale features of the time series. Furthermore, FuzzyEn does not account for coupling characteristics between related or synchronized time series. To address these limitations, a novel entropy-based approach called mu

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24

Doelman, Arjen, Peter van Heijster, and Jianhe Shen. "Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2117 (2018): 20170183. http://dx.doi.org/10.1098/rsta.2017.0183.

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In this article, a general geometric singular perturbation framework is developed to study the impact of strong, spatially localized, nonlinear impurities on the existence, stability and bifurcations of localized structures in systems of linear reaction–diffusion equations. By taking advantage of the multiple-scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single- and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-)pulse solution. In the scalar case, we show how eigenvalues m

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25

Wertheim, Kenneth Y., Bhanwar Lal Puniya, Alyssa La Fleur, Ab Rauf Shah, Matteo Barberis, and Tomáš Helikar. "A multi-approach and multi-scale platform to model CD4+ T cells responding to infections." PLOS Computational Biology 17, no. 8 (2021): e1009209. http://dx.doi.org/10.1371/journal.pcbi.1009209.

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Immune responses rely on a complex adaptive system in which the body and infections interact at multiple scales and in different compartments. We developed a modular model of CD4+ T cells, which uses four modeling approaches to integrate processes at three spatial scales in different tissues. In each cell, signal transduction and gene regulation are described by a logical model, metabolism by constraint-based models. Cell population dynamics are described by an agent-based model and systemic cytokine concentrations by ordinary differential equations. A Monte Carlo simulation algorithm allows i

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Zhang, Shu, Joseph Bentsman, Xinsheng Lou, Carl Neuschaefer, Yongseok Lee, and Hamza El-Kebir. "Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed." Energies 13, no. 7 (2020): 1759. http://dx.doi.org/10.3390/en13071759.

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Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input

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Chen, Yong Xiang, Jin Biao Liu, and Nan Zhang. "Research on Supply Chain Network System Based on Industrial Cluster." Applied Mechanics and Materials 587-589 (July 2014): 1907–11. http://dx.doi.org/10.4028/www.scientific.net/amm.587-589.1907.

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The reliability of supply chain network system design and optimization based on the industrial cluster was discussed, that is, the operational platform of multi-objective supply chain network was moved to industrial cluster, so the platform has the effects of both regional radiation and scale of economy. Instead of some static research methods such as former traditional mathematic planning, systematic and dynamic analysis, this paper put forward a coordinative mechenism construction, this mechenism used dynamic simulation method which combined the supply chain system with industrial cluster mu

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Liu, Yan, Kai Ma, Hao He, and Kuan Gao. "Obtaining Information about Operation of Centrifugal Compressor from Pressure by Combining EEMD and IMFE." Entropy 22, no. 4 (2020): 424. http://dx.doi.org/10.3390/e22040424.

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Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomp

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Luchinsky, Dmitry G., Vasyl Hafiychuck, Kevin R. Wheeler, et al. "Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V." Thermo 2, no. 3 (2022): 116–48. http://dx.doi.org/10.3390/thermo2030011.

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Nonlinear shrinkage of the metal part during manufacturing by bound metal deposition, both on the ground and under microgravity, is considered. A multi-scale physics-based approach is developed to address the problem. It spans timescales from atomistic dynamics on the order of nanoseconds to full-part shrinkage on the order of hours. This approach enables estimation of the key parameters of the problem, including the widths of grain boundaries, the coefficient of surface diffusion, the initial redistribution of particles during the debinding stage, the evolution of the microstructure from roun

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Crouseilles, Nicolas, Shi Jin, and Mohammed Lemou. "Nonlinear geometric optics method-based multi-scale numerical schemes for a class of highly oscillatory transport equations." Mathematical Models and Methods in Applied Sciences 27, no. 11 (2017): 2031–70. http://dx.doi.org/10.1142/s0218202517500385.

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We introduce a new numerical strategy to solve a class of oscillatory transport partial differential equation (PDE) models which is able to capture accurately the solutions without numerically resolving the high frequency oscillations in both space and time. Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and other highly oscillatory waves. Our first main idea is to use the geometric optics ansatz, which builds the oscillatory phase into an independent variable. We then choose suitable initial data, based on the Chapman–Enskog expansion, for the new mod

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31

Ling, Liwen, Dabin Zhang, Amin W. Mugera, Shanying Chen, and Qiang Xia. "A Forecast Combination Framework with Multi-Time Scale for Livestock Products’ Price Forecasting." Mathematical Problems in Engineering 2019 (October 20, 2019): 1–11. http://dx.doi.org/10.1155/2019/8096206.

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China’s livestock market has experienced exceptionally severe price fluctuations over the past few years. In this paper, based on the well-established idea of “forecast combination,” a forecast combination framework with different time scales is proposed to improve the forecast accuracy for livestock products. Specifically, we combine the forecasts from multi-time scale, i.e., the short-term forecast and the long-term forecast. Forecasts derived from multi-time scale introduce complementary information about the dynamics of price movements, thus increasing the diversities within the modeling p

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Ge, Hao, and Hong Qian. "Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond." Journal of The Royal Society Interface 8, no. 54 (2010): 107–16. http://dx.doi.org/10.1098/rsif.2010.0202.

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A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation s

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Chen, Xiaolong, Hongfeng Zhang, Cora Un In Wong, and Zhengchun Song. "Adaptive Multi-Timescale Particle Filter for Nonlinear State Estimation in Wastewater Treatment: A Bayesian Fusion Approach with Entropy-Driven Feature Extraction." Processes 13, no. 7 (2025): 2005. https://doi.org/10.3390/pr13072005.

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We propose an adaptive multi-timescale particle filter (AMTS-PF) for nonlinear state estimation in wastewater treatment plants (WWTPs) to address multi-scale temporal dynamics. The AMTS-PF decouples the problem into minute-level state updates and hour-level parameter refinements, integrating adaptive noise tuning, multi-scale entropy-driven feature extraction, and dual-timescale particle weighting. It dynamically adjusts noise covariances via Bayesian fusion and uses wavelet-based entropy analysis for adaptive resampling. The method interfaces seamlessly with existing WWTP control systems, pro

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Rizzo, Fabio, Chiara Bedon, Sulyman Mansour, et al. "Dynamics of a Flexible Roof Test Model under Ambient Vibrations Measurements." Applied Sciences 13, no. 7 (2023): 4135. http://dx.doi.org/10.3390/app13074135.

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Flexible roofs are sensitive to wind actions because they are light, and their deformability can induce local or global instability. In most cases, their design requires experimental wind tunnel testing to investigate the aeroelastic phenomena and the structural response under the wind. However, the reduced scale necessary in wind tunnels makes the dynamic identification of the test model difficult. Several approaches of multi-modal dynamic identification can be used, even if a specific approach is not defined for geometric nonlinear flexible roofs. Many times, the choice of the position of th

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Xu, Chao, Chen-Chen Huang, and Wei-Dong Zhu. "Bolt loosening detection in a jointed beam using empirical mode decomposition–based nonlinear system identification method." International Journal of Distributed Sensor Networks 15, no. 9 (2019): 155014771987565. http://dx.doi.org/10.1177/1550147719875656.

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In this work, a state-of-art nonlinear system identification method based on empirical mode decomposition is utilized and extended to detect bolt loosening in a jointed beam. This nonlinear system identification method is based on identifying the multi-scale dynamics of the underlying system. Only structural dynamic response signals are needed to construct a reduced-order model to represent the system concerned. It makes the method easy to use in practice. A new bolt loosening identification procedure based on the constructed system nonlinear reduced-order model is proposed. A new damage featu

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Xiao, Zhenyu, and Zhaoyang Duan. "Observer Design for State and Parameter Estimation for Two-Time-Scale Nonlinear Systems." Processes 12, no. 12 (2024): 2875. https://doi.org/10.3390/pr12122875.

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The design and calculation of nonlinear observers for parameter estimation in multi-time-scale nonlinear systems present significant challenges due to the inherent complexity and stiffness of such systems. This study proposes a framework for designing observers for two-time-scale nonlinear systems, with the objective of overcoming the aforementioned challenges. The design procedure involves reducing the original two-time-scale nonlinear system to a lower-dimensional model that captures only the slow dynamics while approximating the fast states through the use of an algebraic slow motion invari

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Yang, Yi, Hang Li, and Yiping Dai. "Nonlinear vibration characteristics of spur gear system subjected to multiple harmonic excitations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 17 (2019): 6026–50. http://dx.doi.org/10.1177/0954406219858171.

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Due to the complicated working conditions, the gear systems are often subjected to multifrequency excitations in practical situations. This paper is concerned with the nonlinear vibration behaviors of a spur gear pair to excitations that involve multiple frequencies. The spur gear system is described by a typical single degree of freedom model, in which the nonlinear backlash, static transmission error, and multiple harmonic excitations are taken into consideration. With the help of the multi-scale method, the nonlinear frequency–response characteristics of the spur gear system are derived and

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Kuske, R., and D. Yurchenko. "Editorial." European Journal of Applied Mathematics 30, no. 5 (2019): 829. http://dx.doi.org/10.1017/s0956792518000694.

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The origin of this special issue took place at the 9th European Nonlinear Dynamics Conference (ENOC 2017) in Budapest, Hungary. Specifically, the mini-symposium on Random Dynamical Systems – Recent Advances and New Directions brought together novel perspectives on analyzing stochastic dynamics with applications including biology, structural dynamics, control, energy and mechanics. The expanded use of stochasticity in more realistic models exposes questions related to bifurcations, meta-stability, tipping and early warning signals, multiscale dynamics, and connections between chaos and stochast

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Vakakis, Alexander F. "Passive nonlinear targeted energy transfer." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (2018): 20170132. http://dx.doi.org/10.1098/rsta.2017.0132.

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Nonlinearity in dynamics and acoustics may be viewed as scattering of energy across frequencies/wavenumbers. This is in contrast with linear systems when no such scattering exists. Motivated by irreversible large-to-small-scale energy transfers in turbulent flows, passive targeted energy transfers (TET) in mechanical and structural systems incorporating intentional strong nonlinearities are considered. Transient or permanent resonance captures are basic mechanisms for inducing TET in such systems, as well as nonlinear energy scattering across scales caused by strongly nonlinear resonance inter

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Castiglioni, Paolo, Stefano Omboni, Gianfranco Parati, and Andrea Faini. "Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis." Entropy 22, no. 4 (2020): 462. http://dx.doi.org/10.3390/e22040462.

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Recently, a multifractal-multiscale approach to detrended fluctuation analysis (DFA) was proposed to evaluate the cardiovascular fractal dynamics providing a surface of self-similarity coefficients α(q,τ), function of the scale τ, and moment order q. We hypothesize that this versatile DFA approach may reflect the cardiocirculatory adaptations in complexity and nonlinearity occurring during the day/night cycle. Our aim is, therefore, to quantify how α(q, τ) surfaces of cardiovascular series differ between daytime and night-time. We estimated α(q,τ) with −5 ≤ q ≤ 5 and 8 ≤ τ ≤ 2048 s for heart r

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Ukhorskiy, A. Y., M. I. Sitnov, A. S. Sharma, and K. Papadopoulos. "Combining global and multi-scale features in a description of the solar wind-magnetosphere coupling." Annales Geophysicae 21, no. 9 (2003): 1913–29. http://dx.doi.org/10.5194/angeo-21-1913-2003.

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Abstract. The solar wind-magnetosphere coupling during substorms exhibits dynamical features in a wide range of spatial and temporal scales. The goal of our work is to combine the global and multi-scale description of magnetospheric dynamics in a unified data-derived model. For this purpose we use deterministic methods of nonlinear dynamics, together with a probabilistic approach of statistical physics. In this paper we discuss the mathematical aspects of such a combined analysis. In particular we introduce a new method of embedding analysis based on the notion of a mean-field dimension. For a

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Chakravarty, Sarbarish, and Michael Zowada. "Dynamics of KPI lumps." Journal of Physics A: Mathematical and Theoretical 55, no. 19 (2022): 195701. http://dx.doi.org/10.1088/1751-8121/ac37e7.

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Abstract A family of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation are investigated. These solutions have multiple peaks whose heights are time-dependent and the peak trajectories in the xy-plane are altered after collision. Thus they differ from the standard multi-peaked KPI simple n-lump solutions whose peak heights as well as peak trajectories remain unchanged after interaction. The anomalous scattering occurs due to a non-trivial internal dynamics among the peaks in a slow time scale. This phenomena is explained by relating the peak locations to the roots of

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Pan, Linyu, and Yuanpeng Zhu. "Grey Model Prediction Enhancement via Bernoulli Equation with Dynamic Polynomial Terms." Symmetry 17, no. 5 (2025): 713. https://doi.org/10.3390/sym17050713.

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The grey prediction model is designed to characterize systems comprising both partially known information (referred to as white) and partially unknown dynamics (referred to as black). However, traditional GM(1,1) models are based on linear differential equations, which limits their capacity to capture nonlinear and non-stationary behaviors. To address this issue, this paper develops a generalized grey differential prediction approach based on the Bernoulli equation framework. We incorporate the Bernoulli mechanism with a nonlinear exponent n and a dynamic polynomial-driven term. In this work,

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de La Parra, Rafael Bravo, Eva Sánchez, and Pierre Auger. "Time Scales in Density Dependent Discrete Models." Journal of Biological Systems 05, no. 01 (1997): 111–29. http://dx.doi.org/10.1142/s0218339097000096.

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The aim of this work is to extend approximate aggregation methods for multi-time scale systems of nonlinear ordinary differential equations to time discrete models. Approximate aggregation consist on describing the dynamics of a general system involving many coupled variables by means of the dynamics of a reduced system with a few global variables. We present discrete time models with two different time scales, the fast one considered linear and the slow one generally nonlinear. We transform the system to make the global variables appear, and use a version of center manifold theory to build up

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Zhang, Ming. "Analyzing the Dynamics and Friction Forces on Spheres in Fluid Flows: Applications Across Engineering and Sports Science." Highlights in Science, Engineering and Technology 119 (December 11, 2024): 671–78. https://doi.org/10.54097/4n9pxn27.

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This study explores the dynamics and friction forces of spherical objects in fluid flows, emphasizing their applications across engineering and sports science. By examining key theoretical concepts such as drag coefficient, Reynolds number, and fluid dynamics equations, the research highlights how these principles influence the motion of spheres in various fluid environments. The analysis encompasses computational fluid dynamics (CFD) and experimental approaches, addressing applications in ocean, aerospace, and vehicle engineering, as well as sports science. The findings demonstrate the critic

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Peng, Zhiyi, and Xiangyu Gu. "Data Structure Trend Prediction Based on XGBoost and DFR Integration." Journal of Computing and Electronic Information Management 17, no. 1 (2025): 33–37. https://doi.org/10.54097/jp7aae88.

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This study proposes a predictive modeling framework based on XGBoost and ensemble learning techniques to forecast national outcomes and structural trends in large-scale competition datasets. First, a multi-dimensional feature system incorporating static, dynamic, and interaction variables is constructed to characterize country-specific attributes. Based on this, an XGBoost-based nonlinear regression model is developed to estimate both gold and total medal counts, while integrating host country effects and event-scale adjustments. Next, to address prediction challenges for countries with sparse

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Ramírez, Adrián, Rifat Sipahi, Sabine Mondié, and Rubén Garrido. "Fast consensus in a large-scale multi-agent system with directed graphs using time-delayed measurements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2153 (2019): 20180130. http://dx.doi.org/10.1098/rsta.2018.0130.

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This article is on fast-consensus reaching in a class of multi-agent systems (MAS). We present an analytical approach to tune controllers for the agents based on the premise that delayed measurements in the controller can be preferable to standard controllers relying only on current measurements. Controller tuning in this setting is however challenging due to the presence of delays. To tackle this problem, we propose an analytic geometry approach. The key contribution is that the tuning can be implemented for complex eigenvalues of the arising graph Laplacian of the network, complementing the

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Sivakumar, B., W. W. Wallender, C. E. Puente, and M. N. Islam. "Streamflow disaggregation: a nonlinear deterministic approach." Nonlinear Processes in Geophysics 11, no. 3 (2004): 383–92. http://dx.doi.org/10.5194/npg-11-383-2004.

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Abstract. This study introduces a nonlinear deterministic approach for streamflow disaggregation. According to this approach, the streamflow transformation process from one scale to another is treated as a nonlinear deterministic process, rather than a stochastic process as generally assumed. The approach follows two important steps: (1) reconstruction of the scalar (streamflow) series in a multi-dimensional phase-space for representing the transformation dynamics; and (2) use of a local approximation (nearest neighbor) method for disaggregation. The approach is employed for streamflow disaggr

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Papageorgiou, Demetrios T., and Saleh Tanveer. "Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (2021): 20210307. http://dx.doi.org/10.1098/rspa.2021.0307.

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This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The on

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Yu, Jiawei, Ziqian Yang, Jurgen Kurths, and Meng Zhan. "Small-Signal Stability of Multi-Converter Infeed Power Grids with Symmetry." Symmetry 13, no. 2 (2021): 157. http://dx.doi.org/10.3390/sym13020157.

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Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to uncover its physical mechanisms for system stability and/or instability (oscillation). In this paper, we first establish a nonlinear model of a multi-converter power system within the DC-link voltage timescale, from the first principle. Then, we obtain a linearized model with the associated characteristic matrix, whose eigenvalues determine the system stabilit

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